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Estimation Of Density For Arbitrarily Censored And Truncated Data

In: Probability, Statistics and Modelling in Public Health

Author

Listed:
  • Catherine Huber

    (Université René Descartes - Paris 5)

  • Valentin Solev

    (Steklov Institute of Mathematics)

  • Filia Vonta

    (University of Cyprus, Department of Mathematics and Statistics)

Abstract

Summary We consider survival data that are both interval censored and truncated. Turnbull [Tur76] proposed in 1976 a nice method for nonparametric maximum likelihood estimation of the distribution function in this case, which has been used since by many authors. But, to our knowledge, the consistency of the resulting estimate was never proved. We prove here the consistency of Turnbull’s NPMLE under appropriate conditions on the involved distributions: the censoring, truncation and survival distributions.

Suggested Citation

  • Catherine Huber & Valentin Solev & Filia Vonta, 2006. "Estimation Of Density For Arbitrarily Censored And Truncated Data," Springer Books, in: Mikhail Nikulin & Daniel Commenges & Catherine Huber (ed.), Probability, Statistics and Modelling in Public Health, pages 246-265, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-26023-5_16
    DOI: 10.1007/0-387-26023-4_16
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